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20 OPTICAL PROJECTION fracts it to /2: then the distance between F and /2 repre- sents the aberration of the D h combination. But, owing to the curvature, away from the lens D, of the meniscus d, the marginal ray passes through d nearer the centre than through h, and consequently its second refraction by such a lens is less on that account; the same ray also passes through the meniscus at a less angle of incidence, which in another way also reduces the second refraction. Consequently, the marginal focus is lengthened, and the aberration is reduced to the distance from P to /. The main factor in this correction is the bending away from each other at the margins of the two lenses, which is obtained equally in the double piano form, and explains its superiority to the two double convex lenses, c, fig. 10. But it will be evident that the other condition, of ' minimum devia- tion ' at the margin, is only ap- proximated to when the curves or thicknesses of the lenses are in some proportion to the foci on each side of the condenser (i.e. the position of the radiant, and the position of its image on the other side of the condenser). Hence, for a lime-light condenser, the lens next the radiant should be of considerably deeper curve, the two lenses taking the form of fig. 12 rather than of E in fig. 10. Then the spherical aberration F/ will also be comparatively smaller. A thicker lens, however, is more in danger of cracking from the heat; therefore, as it will be obvious that a somewhat smaller diameter at d d will collect all the bundle of diverging rays which can reach the second lens, D, this fact should be taken advantage of, in order to reduce its thickness while keeping the deeper curve (see fig. 13). All things considered, I regard this as practically the best